[Feature] Show current connection details in Settings page

[dragnot]

Summary

The Settings page currently does not display the host/IP, port, or username of the currently connected FalkorDB instance. While some connection info is shown in the Header sidebar (as tooltips), it is not prominently visible in Settings.

When working with multiple FalkorDB instances, it's hard to tell which one you're connected to at a glance.

Proposed Change

Add a section to the Settings page that clearly displays:

• Host / IP of the connected FalkorDB instance
• Port
• Username of the authenticated user
• Connection type (Standalone / Sentinel / Cluster)

Context

• Connection info is currently only shown in the Header component via tooltips (e.g., hovering over connection type badges)
• Past issues ([Browser] Display falkordb version of connected database #1281, [Browser] Customer/Generic - add graph serving server IP/Endpoint to Graph Info panel and Manage Graph table #1287, [Browser] Add endpoint, version of browser to left panel #1473) added endpoint and version info to the left panel, but the Settings page itself still lacks this information
• The Settings page (app/settings/page.tsx) has tabs for Browser Settings, DB Configurations, Users, and Personal Access Tokens — none of which surface connection details

Use Case

Users managing multiple FalkorDB environments (dev, staging, production) need a clear, always-accessible view of which instance they are currently connected to.

[overcut-ai]

Completed Working on "Automated Ticket Triage "

✅ Triage complete for issue #1595. Applied label: feature. No duplicate was identified (closest match: #1518, similarity ~0.18). No needs-info label was applied because the issue contains sufficient detail for categorization.

✅ Workflow completed successfully.

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